Such a 3D image dataset is obtained when a plurality of 2D image datasets are recorded. For this purpose a unit consisting of X-ray radiation source and X-ray radiation detector must be moved in unison successively into a plurality of rotational positions about an axis of rotation, and a 2D image dataset is acquired at each rotational position.
Calculating the 3D image dataset is very simple if the rotational positions encompass the entire range of 360° in equal increments. Frequently, however, there is merely what is termed a short-scan or partial circle scanning trajectory, with scanning taking place over a range of 200° for example. Then the data are redundant, but not to the same extent. For example, image data acquired at the angle of 10° correspond to data at an interval around 190°. With mutually corresponding image data the positions of X-ray radiation source and a respective detector element are simply interchanged, yet the X-ray beams pass through the image object simply in the reverse direction, but on the same paths. It is self-evident that these redundancies in the calculation of a 3D image dataset associated with the image object need to be eliminated.
The technique according to Feldkamp known as filtered backprojection exists for such partial circle scanning trajectories, wherein the redundancy is removed by means of a weighting of the detector content, said weighting being referred to as the Parker weights. Although computationally efficient, this approach only contains approximations. So-called cone beam artifacts are visible in the thus resulting 3D image dataset.
It is known from the publication by Zhu et al., “A short-scan reconstruction for cone-beam CT using shift-invariant FBP and equal weighting”, Med. Phys. 34 (11), November 2007, pages 4422 to 4438, to eliminate the redundancies as follows: A filtered backprojection is performed in respect of the 2D image dataset in order to acquire a first 3D image dataset in which mutually corresponding data from the 2D image datasets are possibly incorporated twice (i.e. once redundantly). Said redundancy is now compensated for as follows: An additional calculation is performed in order to acquire a second 3D image dataset on the basis of the 2D image datasets, in which calculation the data included twice in the first 2D image dataset are not incorporated at all. The two 3D image datasets are then averaged, such that all the data are included once in the resulting 3D image dataset.
In this way a method according to the preamble of the independent claim is obtained.
A disadvantage of the method of Zhu et al. is that the problem referred to as axial truncation is only dealt with approximately. Compared to the Feldkamp approach, image errors are produced at the top and bottom end of the field of view. Furthermore it does not permit the volume to be calculated only in sections of axial layers.
The article by Arai et al., “A New Class of Super-Short-Scan Algorithms for Fan-Beam Reconstruction”, IEEE Medical Imaging Conference Record, Wyndham El Conquistador, Puerto Rico, pages 2296 to 2300 (2005), describes an image reconstruction algorithm in which a Hilbert transform is followed by a derivation.